Another Look at the Safety Effects of Horizontal Curvature on Rural Two-Lane Highways

Transcription

1 1 2 Another Look at the Safety Effects of Horizontal Curvature on Rural Two-Lane Highways Taha Saleem (Corresponding Author) Ryerson University Department of Civil Engineering 350 Victoria Street, Toronto, Canada M5B2K3 Phone: Fax: taha.saleem@ryerson.ca Bhagwant Persaud Ryerson University Department of Civil Engineering 350 Victoria Street, Toronto, Canada M5B2K3 Phone: , Ext 6464 Fax: bpersaud@ryerson.ca Word count: (3 figures + 6 tables) = 5660 words Submission date: August 1, 2015

2 Saleem & Persaud ABSTRACT Crash Modification Factors (CMFs) are used to represent the effects on crashes of changes to highway design elements and are usually obtained from observational studies based on reported crashes. The design element of interest for this paper is horizontal curvature on rural 2-lane highways. Crash prediction models are developed for curve sections on rural 2-lane highway and the tangent up and down stream of the curve sections and their predictive capabilities are evaluated. The relationship between crashes at different traffic volumes and deflection angles are explored to get approximate estimates of CMFs for increases in the minimum radius (by factors of 1.10, 1.25, 1.50, and 2.00) considering the effects of increased tangent lengths for sharper curves. The overall results indicate that even at different design speeds and deflection angles, the CMF estimates for incremental increases in radius lie within the same range. Keywords: Crash Prediction Models, Curve Flattening, Crash Modification Factors, Horizontal Curves.

3 Saleem & Persaud INTRODUCTION Crash Modification Factors (CMFs) are used to represent the effects on crashes of changes to highway design elements and are usually obtained from observational studies based on reported crashes. Observational studies can be classified into before-after and cross-sectional studies. CMFs derived from before-after studies are based on the change in safety due to the implementation of a treatment, whereas, CMFs from cross-sectional studies are developed in essence by comparing the safety of a group of sites with a feature with that of a group of sites without that feature, typically utilizing safety prediction models to control for the effects of other differences between the two groups. These models estimate the expected number of crashes per year for an entity using variables such as the average annual daily traffic (AADT), and geometric and traffic control features. The design element of interest for this paper is flattening of horizontal curves on rural 2- lane highways. The most well known and perhaps widely used model for predicting safety on rural 2-lane highways was developed by Zegeer et al. (1992) [1]. Zegeer et al. in their paper looked at the safety effects of various geometric improvements on horizontal curves. A study conducted by Hauer et al. (2000) [2] concluded that the model developed by Zegeer et al. was the most useful and accurate model to account for safety on horizontal curves on rural 2-lane highways. Hauer et al. in their study expressed the Zegeer et al. s model as a CMF, which was subsequently adopted by the Highway Safety Manual (2010) [3] to represent the effect of horizontal curvature changes. Many recent researchers have also tried to analyze safety on horizontal curves. Pitale et al. (2009) [4] analyzed using in-vehicle technologies as means of reducing crashes along horizontal curves. Fitzpatrick et al. (2009) [5] modeled horizontal curve safety with consideration for driveway density, whereas, Schneider et al. (2009) [6] analyzed the effects of horizontal curves on truck safety. Zegeer et al. s [1] model as adapted as a CMF by Highway Safety Manual [3] does not provide any interaction between horizontal curvature and the percent grade on rural 2-lane highways, and although the Highway Safety Manual [3] has a separate CMF representing the safety effects of percent grade, it does not provide any method to account for the interaction between curvature and grade. Thus, technically the horizontal curvature CMF presented in the Highway Safety Manual [3] assumes that horizontal curvature effects safety in the same way whether it is located on level roadway (0% grade), level grade ( 3%), moderate grade (3-6%), or steep grade ( 6%). Bauer & Harwood (2013) [7] in their study tried to address this issue by analyzing the safety affects for horizontal curve and grade combinations. They modeled horizontal curves on straight grades (both level and non-level alignments) with percent grades ranging from 0% to 9.67%. Furthermore, the CMF presented in the Highway Safety Manual does not consider differences in tangent lengths, although Zegeer et al. [1] did develop a tangent model and suggested how it could be used when estimating the safety effect of changing horizontal curvature. The main objective of this study is to explore the development of crash modification function (CMFunction) to estimate CMFs in the scenario where different designs are explored to flatten an existing horizontal curve. This paper builds upon previous research by Zegeer et al. [1] and Bauer & Harwood [7]. This paper tries to improve the linear relationship between crashes and volume as shown by Zegeer et al. [1] and focuses only on curves on level grade ( 3%) so that the approach to developing CMFunctions for changing horizontal curvature could be explored without the confounding effects of harsh gradient.

4 Saleem & Persaud For the purpose of this paper, crash prediction models were developed for (a) the curve sections incorporating the effects of radius, length, and shoulder width, and (b) the tangent sections up and down stream of the curve sections in question. The presentation of these models is then followed by a discussion of how these models can be used as functions to derive the crash reduction rate (CRR) for contemplated changes in design and subsequently the CMFs. To further demonstrate the capabilities of the developed models, the relationship between crashes at different volumes and deflection angles were explored to get approximate estimates of CMFs for incremental increases in the radius, considering the differences in tangent lengths for two different radii. SUMMARY OF DATA The data for this study came from the Washington State database in the Highway Safety Information System (HSIS) [8]. The database consisted of over 11,200 km (7,000 mi) of data including roadway inventory, traffic volumes, crashes and curve/grade information. Some guidelines were set to select the sites that were to be used for the study. These guidelines were as follows; 1. Roadway type should be rural 2-lane highways. 2. Curves should be on grades of 3% or less (absolute) grade to eliminate the confounding effects of harsh grade. 3. Minimum curve radius should be 30.5 m (100 ft.). 4. Maximum curve radius should be 3493 m (11460 ft.). 5. Posted Speed on the curve section should be between mi./hr (~ km/hr) Using these guidelines a total of 440 curves were selected. The data for tangent sections up and down stream of the curves were also extracted from the database for 299 of the 440 curves. Tangent data cannot be extracted for all the 440 curves due to the very small lengths of some tangent sections and in some cases the inability to extract crash data for the particular section. Table 1 shows some summary statistics of these sites. The crash data for these sites were available for the seven-year period from Crash statistics of the sites used in this study can be seen in Table 2. TABLE 1. Summary Statistics for the Curve and Tangent Sections Curve Sections (n = 440) Variable Minimum Maximum Average AADT Radius (m) Length (m) Shoulder (m) Grade (%) Up and Down Stream Tangent Sections (n = 299) Variable Minimum Maximum Average AADT Length (m) Shoulder (m) Note: 1 mi = m, 1 ft. = m

5 Saleem & Persaud TABLE 2. Crash Statistics for the Curve and Tangent Sections Curve Sections (n = 440) Crash Totals ( ) Minimum Maximum Average Total Fatal & Injury Property Damage Only Up and Down Stream Tangent Sections (n = 299) Crash Totals ( ) Minimum Maximum Average Total Fatal & Injury Property Damage Only MODEL FITTING AND EVALUATION Consistent with state-of-the-art methods, generalized linear modelling, with the specification of a negative binomial (NB) error structure, was used to develop the crash prediction models [9] using the SAS software [10]. The specification of an NB-error structure allows for the direct estimation of the overdispersion parameter (K), which can be used to assess the models since it is directly related to the variance of the predictions. Overdispersion occurs when the data have larger variance than is expected under the assumption of a Poisson distribution. A value of K close to 0 is an indicator of a well-fit model. Other goodness-of-prediction measures were used to assess the predictive capabilities of each model were: Plots of the cumulative residuals (observed minus predicted crash frequencies) graphed versus each variable in the model (called CURE plots), Mean absolute deviation (absolute value of sum of observed minus predicted crash frequencies divided by sample size), and Mean prediction error (square root of the sum of squared differences between observed and predicted crash frequencies divided by sample size). Model Fitting Using Curve Data The model form used for developing the models for curve sections was as follows: Crashes/Year = e α AADT β 1 Radius β 2 Length β 3 e β 4 Shoulder Width (1) Where; AADT = Average annual daily traffic, Radius = Radius of curve in meters, Length = Length of curve in meters, and Shoulder Width = Average of left and right side shoulder widths in meters. Table 3 shows the coefficient estimates, dispersion parameters and the goodness of prediction measures for models for various crash severities. As can be seen from Table 3, the estimates of β1, β2, β3 and β4 have intuitive signs and are all highly significant (P<0.02) for almost all of the models. The goodness of prediction measures also suggest reasonably good fits in that the MAD/year/site (Mean Absolute deviation) and the MPE/year/site (Mean Prediction Error) for all the models are small when compared to the average observed crashes per year per site. For example, the MAD/year/site for total crashes is compared to an average of ~1.18 crashes per year/site.

6 Saleem & Persaud TABLE 3. Coefficient s, Dispersion Parameters & Goodness of Prediction Measures for the Curve Models Crash Type Coefficient α β1 β2 β3 β4 K Total Crashes F&I Crashes PDO Crashes (0.4181) < (0.6732) < (0.5363) < (0.0948) < (0.1523) < (0.1210) < (0.1010) < (0.1628) (0.1299) (0.1138) < (0.1831) (0.1464) < (0.0438) (0.0730) (0.0564) Crash Type Avg. Obs. Crashes/Year/Site MAD/Year/Site MPE/Year/Site Total Crashes F&I Crashes PDO Crashes FIGURE 1. CURE Plots for the Curve Models The CURE plots (Figure 1) for AADT for all of the crash models show some over prediction at AADTs of less than 5,000, but apart from that the plots oscillate consistently, showing little or no bias and staying between the 95% confidence boundaries. On the other hand, the CURE plots for radius, the key variable in this study, show that the cumulative residuals lie within the 95% confidence boundaries and oscillate consistently showing little or no bias.

7 Saleem & Persaud Model Fitting Using Up and Downstream Tangent Data The model form used for developing the models for tangent sections was as follows: Crashes/Year = e α AADT β 1 Length β 2 (2) Where; AADT = Average annual daily traffic, and Length = Length of tangent section in meters (average of the upstream and downstream sections). Table 4 shows the coefficient estimates, dispersion parameters and the goodness of prediction measures for models distinguished by their specific crash types. Note that shoulder width is not included in this model because it had a small and insignificant effect. TABLE 4. Coefficient s, Dispersion Parameters & Goodness of Prediction Measures for the Tangent Models Crash Type Total Crashes F&I Crashes PDO Crashes Coefficient α (0.5690) < (0.8499) < (0.7562) < β (0.1256) < (0.1900) < (0.1648) < β (0.0845) < (0.8237) < (0.1142) < K Crash Type Total Crashes F&I Crashes PDO Crashes Avg. Obs. Crashes/Year/Site MAD/Year/Site MPE/Year/Site FIGURE 2. CURE Plots for the Tangent Models As can be seen from Table 4, the estimates of β1 and β2 are highly significant (P<0.01) for all the models. The goodness of prediction measures also suggest reasonably good fits in that the MAD/year/site (Mean Absolute deviation) and the MPE/year/site (Mean Prediction Error) for all

8 Saleem & Persaud the models are small when compared to the average observed crashes per year per site. For example, the MAD/year/site for total crashes is compared to an average of ~0.5 crashes per year/site. The CURE plots (Figure 2) for all of the crash models on tangent sections lie between the 95% confidence boundaries and oscillate consistently, showing little or no bias. APPLICATION OF CRASH PREDICTION MODELS FOR ESTIMATING CRASH MODIFICATION FACTORS FOR CURVE FLATTENING In order to assess the safety impacts of flattening a curve, it is essential to analyse the study area that extends beyond the limits of the smaller radii curve. The reason behind this is that when a curve is flattened (i.e. going from a small radii to a larger radii), tangent sections from either ends are taken away to pave way for the larger radii curve. This phenomenon is further illustrated in Figure 3 used by Hauer (1999) [11] in his paper. Thus, to accurately compare crashes between the old curve and the flattened curve, one should also account for crashes on the tangent section that was removed to accommodate the longer length of the flattened curve. Curved segments with spirals were considered in calculating tangent lengths for the entire curved segment, and the spiral lengths were added to the curve length to apply the models to equation FIGURE 3. Illustration of Curve Flattening (going from to 1-I-1 ) for a given Deflection Angle [11] Crash Reduction Rate (CRR) & Crash Modification Factor (CMF) Estimation Methodology The crash reduction rate could be simply found by using the following equation; CRR = Crashes old section Crashes new section Crashes old section (3) When going from a small radii curve to a larger radii curve the crashes on the old section consist of crashes on the old curved segment and the crashes on the old tangent segments. The crashes on the new section would simply be the crashes on the flattened curve section with the larger radii. The curved segment to which the model is applied would include the circular curve plus the spirals, where these are used. Using the models shown in equations 1 and 2, we can derive the total crashes on curves and tangent sections using the following equations: C Curve = e AADT Radius Length e Shoulder Width (4) C Tangent = e AADT Length (5)

9 Saleem & Persaud Using equations 4, 5, and 6 we can derive the crash modification function (CMFunction) that could be used to assess different scenarios of curve flattening and get a crash modification factor (CMF) for them. CMFunction = 1 (C old curved segment+c old tangent ) C new curved segment (C old curved segement +C old tangent ) CMF s for Incrementally Increasing Radius over the Minimum Value Required at Certain Design Speeds The Transportation Association of Canada s Geometric Design Guide for Canadian Roads [12] specifies minimum radius requirements for different design speeds at different super elevation rates. For this study, the maximum super elevation rate of 0.06m/m was used because, according to [12], in rural areas, the maximum super elevation rate of 0.06m/m is gaining more acceptance as it results in better horizontal alignment consistent with driver expectations for cases where minimum radii are used. In this section, minimum radius for design speeds of 80, 90, and 100 km/h were used as the base case to derive CMFs for increasing the radius by a factor of 1.10, 1.25, 1.50, and 2.00 over the minimum radius at different AADTs (15 th, 50 th and the 85 th percentile of the dataset) and deflection angles. Spiral lengths specified in the TAC guide [12] for the appropriate radii were used. The results of this analysis are shown in Table 5. TABLE 5. Total Crashes CMF Estimations for Certain Increases in the Radius beyond Minimum Values Design Speed = 80 km/h ; Minimum Radius = 250 m (Base Case: CMF = 1) AADT Def. Angle R min R min x R min x R min x R min x Design Speed = 90 km/h ; Minimum Radius = 340 m (Base Case: CMF = 1) AADT Def. Angle R min R min x R min x R min x R min x Design Speed = 100 km/h ; Minimum Radius = 440 m (Base Case: CMF = 1) AADT Def. Angle R min R min x R min x R min x R min x (6)

10 Saleem & Persaud It can be clearly seen that the CMF estimates for a certain design speed and deflection angle follow a similar trend irrespective of the AADT. For example, at a design speed of 80 km/h, the CMF for increasing the radius by a factor 1.50 at deflection angle of 90 0 is ~0.740 irrespective of the AADT. Similarly, at a design speed of 100 km/h, the CMF for increasing the radius by a factor of 2 at deflection angle of 30 0 is ~0.680, irrespective of the AADT. It can also be seen that even at different speeds, the CMF estimate for a certain scenario seems to be following a similar trend. Table 6 summarizes the average approximate crash reduction rate (derived from Table 5) irrespective of the design speeds and AADTs for a specified increase in radius. These results are comparable to those found by Zegeer et al. [1] and Hauer [11]. They concluded that the greater the curve flattening is, the higher is the reduction in crashes is. Our results show an average crash reduction of between 25% - 45% for an increase in radius by a factor of 2 compared to an average crash reduction of between 15% -25% for an increase in radius by factor of These results are reasonably consistent with the average crash reduction of 35% - 55% found by Zegeer et al. [1] for increasing the radius by a factor of 2. TABLE 6. Average Crash Reduction Rate (CRR) from the Results in Table 5 Def. Angle CRR for R min x % - 15% 5% - 20% 10% - 20% 15% - 25% CRR for R min x % - 20% 15% - 25% 20% - 25% 20% - 30% CRR for R min x % - 25% 20% - 30% 25% - 35% 30% - 35% CRR for R min x % - 35% 30% - 35% 30% - 40% 35% - 45% The results shown in Tables 5 and 6 also support Hauer s [11] argument in that the CMF estimates for a certain scenario are approximately the same (i.e. they lie in the same average range) irrespective of the value of radius chosen as the base case. SUMMARY This paper provides new insights into estimating CMFs for flattening an existing horizontal curve on rural 2-lane highways on grades less than 3%. Crash prediction models were developed for the curve sections and also the tangents up and down stream of the curve sections. These models were statistically significant to the 5% level and had low standard errors. The goodness of prediction measures also suggested of a good fit. To further demonstrate the capabilities of this approach, the relationship between crashes at different volumes and deflection angles were explored to get approximate estimates of CMFs for increasing the minimum radius required by a factor of 1.10, 1.25, 1.50, and In this case, to accurately compare crashes between the old curve and the flattened curve, crashes on the tangent section that was removed to accommodate the longer length of the flattened curve were also taken into account. The results show that even at different design speeds, the CMF estimates for a certain scenario lie in the same range. There are a few limitations of the research presented in this paper that need to be addressed in future. The first is the absence of consideration for the presence of spiral as was modelled by Zegeer et al. [1]. The presence of spirals was not available in the dataset that was used and hence in the future, once more data is received, work can/will be done to incorporate the presence of spirals in the model. The second limitation of the models is that the length of tangent to the preceding curve was not used as a variable in the curve model. The reason it was excluded was

11 Saleem & Persaud because the coefficient estimate for this tangent length showed a negligible effect on crashes. The last limitation of the models is that they apply to grades less than 3%. Given the promise of the approach future work can estimate CMFs for flattening curves for other grade ranges. ACKNOWLEDGEMENTS The authors of this paper would like to thank the staff at Highway Safety Information System for providing the data without which this research would not have been possible. This research was supported by discovery grants from the Natural Sciences and Engineering Research Council of Canada. REFERENCES 1. Zegeer, C., Stewart, J., Council, F., Reinfurt, D., and Hamilton, E., (1992). Safety Effects of Geometric Improvements on Horizontal Curve. Transport Research Record: Journal of the Transportation Research Board, No. 1356, pp , Hauer, E., Harwood, D.W., Council, F.M., Hughes, W.E., and Vogt, A. (2000). Prediction of the Expected Safety Performance of Rural Two-Lane Highways, Report No. FHWA-RD , Federal Highway Administration, Washington, DC. 3. American Association of State Highway and transportation Officials. (2010). Highway Safety Manual, 1 st Edition, AASTHO, Washington, DC. 4. Pitale, J.T., Shankwitz, C., Preston, H., and Barry, M. (2009). Benefit-Cost Analysis of In- Vehicle Technologies and Infrastructure Modifications as a Means to Prevent Crashes along Curves and Shoulders. Minnesota Department of Transportation. 5. Fitzpatrick, K., Lord, D., and Park, B.J.(2009). Horizontal Curve Accident Modification Factor with Consideration of Driveway Density on Rural, Four-Lane Highways in Texas. TRB 88th Annual Meeting Compendium of Papers CD-ROM. Washington, DC. 6. Schneider, W.H., Zimmerman, K., Boxel, D.V., and Vavilikolanu, S. (2009). A Bayesian Analysis of the Effect of Horizontal Curvature on Truck Crashes Using Training and Validation Data Sets. TRB 88th Annual Meeting Compendium of Papers CD-ROM. Washington, DC. 7. Bauer, K., and Harwood, D., (2013). Safety Effects of Horizontal Curve and Grade Combinations on Rural Two-Lane Highways. Report No. FHWA-HRT , Federal Highway administration, Washington, DC. 8. HSIS (2015). Highway Safety Information System. Available Online at: 9. Persaud, B., Saleem, T., Lyon, C., and Chen, Y., (2012). Safety Performance Functions for Estimating the Safety Benefits of Proposed or Implemented Countermeasures. A report prepared for Transport Canada under Canada s National Road Safety Research and Outreach Program, Ryerson University, SAS (2013). SAS: Enterprise Guide. Available Online at: Hauer, E., (1992). Safety and the Choice of Degree of Curve. Transport Research Record: Journal of the Transportation Research Board, No. 1665, pp. 22, TAC (1999). Geometric Design Guide for Canadian Roads. Transportation Association of Canada, Ottawa.